Firewall mods + Port Scan

As for Port scan protection, like the description there says, it detects and blocks attempts to find out which ports are open. Port scans are frequently used by hackers to find out which ports are open on your device. They might then break into your device if they find a less secure or vulnerable port. I think that when it comes to a home network, most devices don't need to expose ports to the internet, so open ports should already be minimized.
However, devices like smart home gadgets, gaming consoles, or security cameras could potentially be targeted if ports are unintentionally left open. I think that having port scan protection enabled via the firewall adds an extra layer of defense.

When it comes to a good game experience while running any antivirus, it's generally recommended to make good use of the available profiles, as I think most security solutions provide this option in one form or another. With Bitdefender, you can enable and configure the Game Profile to your liking and this may help improve the overall gaming experience.

https://www.bitdefender.com/consumer/support/answer/2066/

Apart from this, Port scan protection should really not interfere with this, just keep in mind the Home/Office & Stealth Mode setups described above.

OK. I will expand more on this, as far as my knowledge allows.
Some software requires bidirectional communication or incoming connections to function properly (e.g., remote desktop, gaming, video conferencing, or file-sharing applications). With stealth mode enabled, the computer can no longer communicate with such software because it's not visible to those apps. Also, if something goes wrong with your network connectivity, stealth mode can make diagnosing the issue more challenging, as the computer won't respond to basic network diagnostics (e.g., pings). Stealth mode can also make collaboration harder on local networks, such as sharing files or participating in multiplayer games or team applications.
To maintain functionality, you may be required to create exceptions in the firewall for trusted applications, devices, or services, etc.

Furthermore, VPNs or security tools usually rely on network visibility to route traffic or verify connectivity. Stealth mode could disrupt their operation if not configured properly. So, I think it really depends on your system configuration, network settings and other programs and activities that you run on your device. It's up to you if you wish to enable it or leave it disabled, and you can also test it to see how it behaves in the context of your usage of the device.

As for pros, stealth mode prevents your computer from responding to unsolicited network probes or pings, making it harder for attackers to detect its presence. This reduces the likelihood of targeted attacks. It prevents local network devices or external systems from establishing unauthorized connections, adding an extra layer of security against malware, hackers, or unauthorized users. By being "invisible," your computer won't appear on network scans, reducing the chances of exploitation via known vulnerabilities. It also reduces exposure to devices or applications on the local network that may attempt to gather information about your system.

Essentially, I think stealth mode is recommended especially on public or unsecured networks, and when you don't need to interact with local network devices or services. I think it's best to avoid using it if you rely heavily on local network devices or collaborative tools that require discovery and communication, or if configuring exceptions for critical applications is an inconvenience for you. I think an assessment should be made beforehand, for balancing security needs with functionality, then you can decide whether Stealth Mode aligns with your computing environment.
Like I said, Home/Office would be the recommended setup in your case, since you mentioned that you don't have a local network connected to your PC.